Very risky. If she is eligible for DACA, she should apply.
(213) 394-4554 x0 Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
She can do it. TSA is only to check that she is the person holding the ticket. They should not examine her passport beyond the bio/photo page. And, if a TSA officer tried to do that, she should object.
It depends on if she is stopped for any reason. Ordinarily, her Mexican passport may be sufficient identification to allow her on a domestic flight. If for any reason a law enforcement officer needs further identification or if she is accused of committing a crime and is arrested. The situation changes and she may be subject to a deportation proceedings.